Spring-Mass-Damper System Identification

A MATLAB implementation of a classical system identification pipeline for estimating the damping and stiffness parameters of a spring-mass-damper (SMD) system from noisy, sparsely sampled measurement data. Like the aircraft sysID implementation, this serves as a baseline reference — results are intended as a basis of comparison for other system identification methods.

The workflow uses two sequential stages: a Least-Squares Regression (equation-error) method for initial parameter estimates, followed by an Output-Error method for refinement.

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System

The system being identified is a 1D spring-mass-damper:

m*x_ddot + c*x_dot + k*x = F(t)

Rearranged for regression, the parameters identified are:

theta = [-c/m, -k/m, 1/m]

with true values m = 2, c = 0.3, k = 0.2 and a sinusoidal forcing input F(t) = sin(2*pi*t).

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Files

File	Description
massdamper_full.mat	Measured data file (sparse, noisy position measurements)
AYUSH_statespace_smd.m	Supporting file defining the SMD state-space model
oe.m	SIDPAC output-error optimizer (Morelli, NASA Langley)

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Pipeline

Sparse, Noisy Measurements
    │
    ▼
Savitzky-Golay smoothing (sgolayfilt)
    │
    ▼
Spline interpolation  —  resampled to uniform 10 Hz grid
    │
    ▼
Numerical differentiation (deriv)  —  xdot, x_ddot
    │
    ▼
Least-Squares Regression  —  lesq (unconstrained)
    │                        regressor: [xdot, x, u]
    ▼  initial parameter estimates
Output-Error Method  —  oe.m (SIDPAC)
    │                   Modified Newton-Raphson + Simplex fallback
    │                   Full simulation at each iteration
    ▼
Final Parameter Estimates

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Data & Preprocessing Notes

The input data is sparsely sampled (sparcityLevel150) with added random noise. Several preprocessing steps are applied before regression:

• Smoothing: Savitzky-Golay filter (sgolayfilt, order 2, window 21) applied to raw position measurements
• Interpolation: Smoothed data is resampled to a uniform 0.1 s grid via spline interpolation before being passed to oe.m
• Differentiation: Velocity and acceleration are computed from the interpolated signal using deriv

The choice of interpolation method and resampling frequency have a measurable impact on parameter estimation accuracy.

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Dependencies

• MATLAB
• SIDPAC toolbox (oe.m and supporting routines: mnr.m, simplex.m, estrr.m, misvd.m, cvec.m, compcost.m, lesq.m)
• deriv.m — smoothed numerical differentiation
• the other files were for data extraction and parsing of Prof. Brunswicker's spring mass damper data